Debates concerning the character, scope, and warrant of abductive inference have been active since Peirce first proposed that there was a third form of inference, distinct from induction and deduction. Abductive reasoning has been dubbed weak, incoherent, and even nonexistent. Part, at least, of the problem of articulating a clear sense of abductive inference is due to difficulty in interpreting Peirce. Part of the fault must lie with his critics, however. While this article will argue that Peirce indeed left a number of puzzles for interpreters, it will also contend that interpreters should be careful to distinguish discussion of the formal and strictly epistemic question of whether and how abduction is a sound form of inference from discussions of the practical goals of abduction, as Peirce understood them. This article will trace a history of critics and defenders of Peirce’s notion of abduction and discuss how Peirce both fueled the confusion and in fact anticipated and responded to several recurring objections.